Worksheet: The Conservation of Angular Momentum

In this worksheet, we will practice calculating the kinematic properties of an object where the angular momentum of the object is conserved.

Q1:

Three disks can all rotate around an axle. The disks have moments of inertia 𝐼, 𝐼, and 𝐼, where 𝐼=𝐼 and 𝐼=8𝐼, and angular velocities 𝜔, 𝜔, and 𝜔. If 𝜔 increases by 0.5 rad/s, by how much must 𝜔 and 𝜔 change in order to counterbalance the increase in the angular momentum of the other disk? Assume that 𝜔 and 𝜔 change by the same amount.

Q2:

Two asteroids orbiting a star collide and form a single, larger asteroid. The first of the two initial asteroids has an angular momentum of 5.4×10 kg⋅m2/s. The second of the two initial asteroids has an angular momentum of 1.9×10 kg⋅m2/s. What is the angular momentum of the larger asteroid that they form?

  • A1.9×10 kg⋅m2/s
  • B1.4×10 kg⋅m2/s
  • C2.4×10 kg⋅m2/s
  • D5.4×10 kg⋅m2/s
  • E1.0×10 kg⋅m2/s

Q3:

A satellite with a mass of 1,200 kg orbits Earth. The satellite follows an elliptical orbit, so the radial distance of the satellite from the center of Earth changes as it orbits. The angular momentum of the satellite is conserved throughout its orbit.

When the satellite is at a radial distance of 7,900 km from the center of Earth, it moves at a speed of 2.2 km/s . What is the angular momentum of the satellite at this point in its orbit?

  • A2.9×10 kg⋅m2/s
  • B2.1×10 kg⋅m2/s
  • C390 kg⋅m2/s
  • D4.6×10 kg⋅m2/s
  • E2.6×10 kg⋅m2/s

What will the speed of the satellite be when it is at a radial distance of 8,500 km from the center of Earth?

Q4:

The diagram shows a planet in an elliptical orbit around a star. At which of the points i, ii, iii, and iv does the planet have the greatest angular momentum?

  • Ai
  • Biii
  • Civ
  • DThe planet has the same angular momentum at all points.
  • Eii

Q5:

The diagram shows two comets in elliptical orbits around a star. The comets will collide at point 𝐶 to form a single, larger comet. Comet 1 has a mass of 3.5×10 kg. When comet 1 is at point 𝐴, it is a distance of 2.4×10 m away from the star and is moving at a speed of 0.56 km/s. Comet 2 has a mass of 1.9×10 kg. When comet 2 is at point 𝐵, it is a distance of 1.7×10 m away from the star and is moving at a speed of 1.0 km/s.

What will the mass of the larger comet be?

  • A1.6×10 kg
  • B1.8×10 kg
  • C4.1×10 kg
  • D2.3×10 kg
  • E7.0×10 kg

What will the angular momentum of the larger comet be?

  • A3.7×10 kg⋅m2/s
  • B4.7×10 kg⋅m2/s
  • C3.7×10 kg⋅m2/s
  • D4.1×10 kg⋅m2/s
  • E1.2×10 kg⋅m2/s

Q6:

A figure skater spins on an ice rink with his arms outstretched. His moment of inertia is 12.6 kg⋅m2, and his angular velocity is 18 rad/s.

If the figure skater pulls his arms in, his moment of inertia decreases. His angular momentum is conserved. Does his angular velocity increase, decrease, or stay the same?

  • AIt decreases.
  • BIt stays the same.
  • CIt increases.

After pulling his arms in, his moment of inertia is 9.7 kg⋅m2. What is his angular velocity?

Q7:

A planet with a mass of 5.4×10 kg orbits a star. The planet follows an elliptical orbit, so the radial distance of the planet from the star changes as it orbits. The angular momentum of the star is conserved throughout its orbit.

When the planet is at a radial distance of 2.8×10 m from the star, it moves at a speed of 4.7 km/s. What is the angular momentum of the planet at this point in its orbit?

  • A7.1×10 kg⋅m2/s
  • B6.0×10 kg⋅m2/s
  • C4.3×10 kg⋅m2/s
  • D2.5×10 kg⋅m2/s
  • E7.1×10 kg⋅m2/s

What will the radial distance between the planet and the star be when the planet is moving at a speed of 5.5 km/s?

  • A3.3×10 m
  • B2.4×10 m
  • C1.3×10 m
  • D2.8×10 m
  • E1.8×10 m

Q8:

The diagram shows three disks, which can all rotate around an axel. Disks 1 and 3 have the same moment of inertia as each other. Disk 2 has a moment of inertia four times that of disk 1. If the angular velocity of disk 2 increases by 2.0 rad/s, by how much must the angular velocity of disks 1 and 3 change in order to counterbalance the change in the angular momentum of disk 2? Assume that disks 1 and 3 must have the same change in angular velocity as each other.

Q9:

The diagram shows five disks, which can all rotate around an axle. Disks 1, 2, 4, and 5 all have the same moment of inertia. The angular velocity of disk 3 increases by 1.2 rad/s, and the increase in angular momentum of disk 3 is counterbalanced by a change in the angular momentum of disks 1, 2, 4, and 5. A change in angular velocity of 1.8 rad/s takes place for each of disks 1, 2, 4, and 5. What is the ratio of the moment of inertia of disk 3 to that of disk 1?

Q10:

The diagram shows five disks that are all the same size and made of the same material and that can rotate around an axel. If the angular momenta of disks 1, 2, 4, and 5 increase by 35 kg⋅m2/s each, by how much must the angular momentum of disk 3 change in order to counterbalance the increase in the angular momenta of the other four?

Q11:

The diagram shows three disks that are all the same size and made of the same material, and they can rotate around an axle. If the angular momenta of disks 1 and 3 increase by 20 kg⋅m2/s each, by how much must the angular momentum of disk 2 change in order to counterbalance the increase in angular momentum of the other two?

Q12:

The diagram shows five disks that are all the same size and made of the same material and that can rotate around an axel. If the angular momenta of disks 1, 3, and 5 increase by 12 kg⋅m2/s each, by how much must the angular momenta of each of the disks 2 and 4 change in order to counterbalance the increase in the angular momenta of the other three? Assume that disks 2 and 4 must have the same change in angular momentum as each other.

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